From: drowe67 Date: Tue, 7 Oct 2014 02:40:25 +0000 (+0000) Subject: simulation of FEC applied to 450 bit/s codec. Estimate of correctable errors with... X-Git-Url: http://git.whiteaudio.com/gitweb/?a=commitdiff_plain;h=01bfcaf2ea08a63c706eb74230762df1c27f820c;p=freetel-svn-tracking.git simulation of FEC applied to 450 bit/s codec. Estimate of correctable errors with a good code makes it useful to about 0 dB, but more work to be done, e.g. test with a real code, interleaving git-svn-id: https://svn.code.sf.net/p/freetel/code@1878 01035d8c-6547-0410-b346-abe4f91aad63 --- diff --git a/codec2-dev/octave/test_fec.m b/codec2-dev/octave/test_fec.m new file mode 100644 index 00000000..710ec490 --- /dev/null +++ b/codec2-dev/octave/test_fec.m @@ -0,0 +1,406 @@ +% test_fec.m +% David Rowe Oct 2014 +% + +% Simulation to test FDM QPSK combined with FEC. A low rate Codec +% (e.g. 450 bit/s) is transmitted on Nc=4 FDM carriers. FEC parity +% bits are repeated on a seperate block of 4 carriers that is delayed +% in time by Rs symbols (1 second). A (n,k) Read Solomon code that can +% correct (n-k)/2 errors is simulated. + +1; + +% main test function + +function sim_out = ber_test(sim_in, modulation) + Fs = 8000; + + verbose = sim_in.verbose; + Ntrials = sim_in.Ntrials; + Esvec = sim_in.Esvec; + phase_offset = sim_in.phase_offset; + w_offset = sim_in.w_offset; + plot_scatter = sim_in.plot_scatter; + Rs = sim_in.Rs; + hf_sim = sim_in.hf_sim; + nhfdelay = sim_in.hf_delay_ms*Rs/1000; + hf_mag_only = sim_in.hf_mag_only; + n = sim_in.n; + k = sim_in.k; % k message bits + Nc = sim_in.Nc; % number of carriers + + bps = 2; + Nsymb = n/bps; % total number of symbols + Nb = Nsymb/Nc; % length of block of symbols + assert(Nb == floor(Nb), "Nb must be an integer"); + + Nck = (k/n)*Nc; % Number of carriers for data symbols + Ncp = ((n-k)/n)*Nc; % Number of carriers for parity symbols + assert(Nck == floor(Nck), "Number of carriers for data symbols must be an integer"); + assert(Ncp == floor(Ncp), "Number of carriers for parity symbols must be an integer"); + + printf("(n,k)=(%d,%d) Nsymb: %d Nc: %d Nb: %d Nck: %d Ncp: %d\n",n,k,Nsymb,Nc,Nb,Nck,Ncp); + + prev_sym_tx = qpsk_mod([0 0])*ones(1,Nc); + prev_sym_rx = qpsk_mod([0 0])*ones(1,Nc); + + % Init HF channel model from stored sample files of spreading signal ---------------------------------- + + % convert "spreading" samples from 1kHz carrier at Fs to complex + % baseband, generated by passing a 1kHz sine wave through PathSim + % with the ccir-poor model, enabling one path at a time. + + Fc = 1000; M = Fs/Rs; + fspread = fopen("../raw/sine1k_2Hz_spread.raw","rb"); + spread1k = fread(fspread, "int16")/10000; + fclose(fspread); + fspread = fopen("../raw/sine1k_2ms_delay_2Hz_spread.raw","rb"); + spread1k_2ms = fread(fspread, "int16")/10000; + fclose(fspread); + + % down convert to complex baseband + spreadbb = spread1k.*exp(-j*(2*pi*Fc/Fs)*(1:length(spread1k))'); + spreadbb_2ms = spread1k_2ms.*exp(-j*(2*pi*Fc/Fs)*(1:length(spread1k_2ms))'); + + % remove -2000 Hz image + b = fir1(50, 5/Fs); + spread = filter(b,1,spreadbb); + spread_2ms = filter(b,1,spreadbb_2ms); + + % discard first 1000 samples as these were near 0, probably as + % PathSim states were ramping up + + spread = spread(1000:length(spread)); + spread_2ms = spread_2ms(1000:length(spread_2ms)); + + % decimate down to Rs + + spread = spread(1:M:length(spread)); + spread_2ms = spread_2ms(1:M:length(spread_2ms)); + + % Determine "gain" of HF channel model, so we can normalise + % carrier power during HF channel sim to calibrate SNR. I imagine + % different implementations of ccir-poor would do this in + % different ways, leading to different BER results. Oh Well! + + hf_gain = 1.0/sqrt(var(spread)+var(spread_2ms)); + + % Start Simulation ---------------------------------------------------------------- + + for ne = 1:length(Esvec) + EsNodB = Esvec(ne); + EsNo = 10^(EsNodB/10); + + variance = 1/EsNo; + if verbose > 1 + printf("EsNo (dB): %f EsNo: %f variance: %f\n", EsNodB, EsNo, variance); + end + + Terrs = 0; Tbits = 0; + + tx_symb_log = []; + rx_symb_log = []; + errors_log = []; + Nerrs_log = []; + + % init HF channel + + hf_n = 1; + + % simulation starts here----------------------------------- + + for nn = 1: Ntrials + + tx_bits = round(rand(1,n)); + + % modulate -------------------------------------------- + + tx_symb=zeros(Nc,Nb); + + for b=1:Nb + for c=1:Nc + i = (b-1)*Nc + c; + tx_symb(c,b) = qpsk_mod(tx_bits(2*(i-1)+1:2*i)); + if strcmp(modulation,'dqpsk') + tx_symb(c,b) *= prev_sym_tx(c); + prev_sym_tx(c) = tx_symb(c,b); + end + end + end + s_ch = tx_symb; + + % HF channel simulation ------------------------------------ + + if hf_sim + + % separation between carriers. Note this effectively + % under samples at Rs, I dont think this matters. + % Equivalent to doing freq shift at Fs, then + % decimating to Rs. + + wsep = 2*pi*(1+0.5); % e.g. 75Hz spacing at Rs=50Hz, alpha=0.5 filters + + for b=1:Nb + + % apply HF model to data symbol carriers + + for c=1:Nck + ahf_model = hf_gain*(spread(hf_n) + exp(-j*k*wsep*nhfdelay)*spread_2ms(hf_n)); + if hf_mag_only + s_ch(c,b) *= abs(ahf_model); + else + s_ch(c,b) *= ahf_model; + end + hf_model(hf_n, c) = ahf_model; + end + + % apply HF model (time shifted into the future) to parity symbol carriers + + for c=1:Ncp + ahf_model = hf_gain*(spread(hf_n+Rs) + exp(-j*k*wsep*nhfdelay)*spread_2ms(hf_n+Rs)); + if hf_mag_only + s_ch(Nck+c,b) *= abs(ahf_model); + else + s_ch(Nck+c,b) *= ahf_model; + end + hf_model(hf_n, Nck+c) = ahf_model; + end + + hf_n++; + end + end + + for b=1:Nb + for c=1:Nc + tx_symb_log = [tx_symb_log s_ch(c,b)]; + end + end + + % AWGN noise and phase/freq offset channel simulation + % 0.5 factor ensures var(noise) == variance , i.e. splits power between Re & Im + + noise = sqrt(variance*0.5)*(randn(Nc,Nb) + j*randn(Nc,Nb)); + + s_ch = s_ch + noise; + + % de-modulate + + rx_bits = zeros(1, n); + for b=1:Nb + for c=1:Nc + rx_symb(c,b) = s_ch(c,b); + if strcmp(modulation,'dqpsk') + tmp = rx_symb(c,b); + rx_symb(c,b) *= conj(prev_sym_rx(c)/abs(prev_sym_rx(c))); + prev_sym_rx(c) = tmp; + end + i = (b-1)*Nc + c; + rx_bits((2*(i-1)+1):(2*i)) = qpsk_demod(rx_symb(c,b)); + rx_symb_log = [rx_symb_log rx_symb(c,b)]; + end + end + + % Measure BER + + error_positions = xor(rx_bits, tx_bits); + Nerrs = sum(error_positions); + Terrs += Nerrs; + Tbits += length(tx_bits); + errors_log = [errors_log error_positions]; + Nerrs_log = [Nerrs_log Nerrs]; + end + + TERvec(ne) = Terrs; + BERvec(ne) = Terrs/Tbits; + + if verbose + av_tx_pwr = (tx_symb_log * tx_symb_log')/length(tx_symb_log) + + printf("EsNo (dB): %3.1f Terrs: %d BER %4.3f QPSK BER theory %4.3f av_tx_pwr: %3.2f", EsNodB, Terrs, + Terrs/Tbits, 0.5*erfc(sqrt(EsNo/2)), av_tx_pwr); + printf("\n"); + end + if verbose > 1 + printf("Terrs: %d BER %f BER theory %f C %f N %f Es %f No %f Es/No %f\n\n", Terrs, + Terrs/Tbits, 0.5*erfc(sqrt(EsNo/2)), var(tx_symb_log), var(noise_log), + var(tx_symb_log), var(noise_log), var(tx_symb_log)/var(noise_log)); + end + end + + Ebvec = Esvec - 10*log10(bps); + sim_out.BERvec = BERvec; + sim_out.Ebvec = Ebvec; + sim_out.TERvec = TERvec; + sim_out.errors_log = errors_log; + + if plot_scatter + figure(2); + clf; + scat = rx_symb_log .* exp(j*pi/4); + plot(real(scat), imag(scat),'+'); + title('Scatter plot'); + + if hf_sim + figure(3); + clf; + + y = 1:(hf_n-1); + x = 1:Nc; + EsNodBSurface = 20*log10(abs(hf_model(y,:))) - 10*log10(variance); + EsNodBSurface(find(EsNodBSurface < -5)) = -5; + mesh(x,y,EsNodBSurface); + grid + axis([1 Nc 1 Rs*5 -5 15]) + title('HF Channel Es/No'); + + if verbose + av_hf_pwr = sum(abs(hf_model(y)).^2)/(hf_n-1); + printf("average HF power: %3.2f over %d symbols\n", av_hf_pwr, hf_n-1); + end + end + + figure(4) + clf + stem(Nerrs_log) + end + +endfunction + +% Gray coded QPSK modulation function + +function symbol = qpsk_mod(two_bits) + two_bits_decimal = sum(two_bits .* [2 1]); + switch(two_bits_decimal) + case (0) symbol = 1; + case (1) symbol = j; + case (2) symbol = -j; + case (3) symbol = -1; + endswitch +endfunction + +% Gray coded QPSK demodulation function + +function two_bits = qpsk_demod(symbol) + if isscalar(symbol) == 0 + printf("only works with scalars\n"); + return; + end + bit0 = real(symbol*exp(j*pi/4)) < 0; + bit1 = imag(symbol*exp(j*pi/4)) < 0; + two_bits = [bit1 bit0]; +endfunction + +function sim_in = standard_init + sim_in.verbose = 1; + sim_in.plot_scatter = 0; + + sim_in.Esvec = 5; + sim_in.Ntrials = 30; + sim_in.Rs = 50; + sim_in.Nc = 8; + + sim_in.phase_offset = 0; + sim_in.w_offset = 0; + sim_in.phase_noise_amp = 0; + + sim_in.hf_delay_ms = 2; + sim_in.hf_sim = 0; + sim_in.hf_mag_only = 0; +endfunction + +function test_curves + + sim_in = standard_init(); + + sim_in.verbose = 1; + sim_in.plot_scatter = 1; + + sim_in.Esvec = 50; + sim_in.hf_sim = 0; + sim_in.Ntrials = 1000; + + sim_qpsk_hf = ber_test(sim_in, 'qpsk'); + + sim_in.hf_sim = 0; + sim_in.plot_scatter = 0; + sim_in.Esvec = 5:15; + Ebvec = sim_in.Esvec - 10*log10(2); + BER_theory = 0.5*erfc(sqrt(10.^(Ebvec/10))); + sim_dqpsk = ber_test(sim_in, 'dqpsk'); + sim_in.hf_sim = 1; + sim_in.hf_mag_only = 1; + sim_qpsk_hf = ber_test(sim_in, 'qpsk'); + sim_in.hf_mag_only = 0; + sim_dqpsk_hf = ber_test(sim_in, 'dqpsk'); + sim_in.Nchip = 4; + sim_dqpsk_hf_dsss = ber_test(sim_in, 'dqpsk'); + + figure(1); + clf; + semilogy(Ebvec, BER_theory,'r;QPSK theory;') + hold on; + semilogy(sim_dqpsk.Ebvec, sim_dqpsk.BERvec,'c;DQPSK AWGN;') + semilogy(sim_qpsk_hf.Ebvec, sim_qpsk_hf.BERvec,'b;QPSK HF;') + semilogy(sim_dqpsk_hf.Ebvec, sim_dqpsk_hf.BERvec,'k;DQPSK HF;') + semilogy(sim_dqpsk_hf_dsss.Ebvec, sim_dqpsk_hf_dsss.BERvec,'g;DQPSK DSSS HF;') + hold off; + + xlabel('Eb/N0') + ylabel('BER') + grid("minor") + axis([min(Ebvec) max(Ebvec) 1E-3 1]) +endfunction + +function test_1600_v_450 + + sim_in = standard_init(); + + sim_in.verbose = 1; + sim_in.plot_scatter = 1; + sim_in.Ntrials = 500; + sim_in.hf_sim = 1; + + sim_in.framesize = 32; + sim_in.Nc = 16; + sim_in.Esvec = 7; + sim_in.Nchip = 1; + + sim_dqpsk_hf_1600 = ber_test(sim_in, 'dqpsk'); + + sim_in.framesize = 8; + sim_in.Nc = 4; + sim_in.Esvec = sim_in.Esvec + 10*log10(1600/450); + sim_in.Nchip = 4; + + sim_dqpsk_hf_450 = ber_test(sim_in, 'dqpsk'); + + fep=fopen("errors_1600.bin","wb"); fwrite(fep, sim_dqpsk_hf_1600.errors_log, "short"); fclose(fep); + fep=fopen("errors_450.bin","wb"); fwrite(fep, sim_dqpsk_hf_450.errors_log, "short"); fclose(fep); + +endfunction + +function test_single + + sim_in = standard_init(); + + sim_in.verbose = 1; + sim_in.plot_scatter = 1; + + sim_in.n = 48*8; + sim_in.k = 24*8; + snr = 1; + sim_in.Esvec = snr + 10*log10(3000/400); + sim_in.hf_sim = 1; + sim_in.Ntrials = 100; + + sim_qpsk_hf = ber_test(sim_in, 'dqpsk'); +endfunction + + +% Start simulations --------------------------------------- + +more off; + +%test_1600_v_450(); +%test_curves(); +test_single();